I think it mostly equates to using good judgment, instinct and being very watchful of what's going on. Every studio is a little different, so I talk from my own personal experience. It's gonna sound kina dickish, but that's cause I'm sayin just like all my bosses told me.

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The general attitude of a good assistant is that of a loyal servant. It's a lot of bitch work, there's no dancing around that. Alot of "yes sirs" and "I can do that" type words. Alot of painful jobs like making coffee, making food runs for everyone and zeroing out the gear. If you're a free spirit "play by your own rules" kinda guy, you'll have to find a way to suppress that until you branch out on your own. I've gotten in trouble for that many times.
Some notes:
1) Don't expect big strides right away. Have patience. A former colleague of mine, Aaron Gandia, works as the head engineer for a studio called Phat Planet in Orlando. He really busted his ass for a year to get there, so expect a long haul.
2) Get to know your boss. Obviously if you find his sweet spot, you're making brownie points.
3) Learn to wrap a mic cable *properly*. This one actually gets many assistants fired on the first day in some studios.
If the engineer can't lay out the cable without it tangling, there's a good chance that's gonna piss him off. If done properly, you should be able to "uncoil" a cable effortlessly across the floor without any knots.
4) Studios prefer assistants with "multiple" talents. In other words, read up on Martha Stewart's "10 ways to make a great cup of coffee".
5) When dealing with a client, take your cues from your boss and let him do the talking. Trust me on this. I had another colleague of mine that opened his mouth at Madonna and got himself blackballed. He's flippin burgers now. True story.
6)Study during the downtime. Study *everything* about the studio. The patchbays, mic inputs, the console (and the 100 page manual), the inventory, methods...every detail possible.
7)It helps to have knowledge about basic electronics and basic studio repair. The most sought after jobs right now in the studio are technicians. Mixing and recording engineering is a very over saturated market right now. I had a friend of mine who landed himself a nice job at Big Shot Studios here in Orlando because he offered to wire up the studio for free. All it took was some basic soldering know-how. Studios LOVE it when you fix broken mic cables (which are really easy to do if you have a soldering kit).
8)Develop thick skin. You're gonna get yelled at, abused, tortured, chewed out...you name it. Don't take it personal, it can get pretty rough with some of the personalities that exist in the music industry.
Nevermind the long hours with little or no pay. If you stick with it, the benefits will come.
9) I guess it really comes down to this one: just use common sense and try to have fun
If your bosses can see that you're having a good time, getting shit done, show up when asked and taking initiative...you'll get called back, trust me.